Still, this model with particle positions taking center stage is not completely satisfactory, either. For one, the theory deals only with distinguishable particles; and the transition to a theory of indistinguishable particles is not straightforward (see e.g., [1]}[2]}). Another drawback is that the theory is inherently non-relativistic and deals only with a fixed number of particles. This runs counter to the fact that relativistic processes allow for an indefinite number of particles through absorbtion and emission of.On a side note, despite its success, it is certainly possible that the principles of relativity might break down. In recent years this possibility has inspired some to develop models where the usual Lorentz invariance is violated (see e.g., [3]}[4]}[5]}[6]}). To date, however, there does not seem to be any empirical support for these claims. (For an older review of Lorentz invariance violations, see e.g., [7]}). Thus for the time the principle of relativity appears safe as a fundamental symmetry. Moreover, there is strong evidence that the notion of a particle might itself be a fraught concept (see e.g., [8]}[9]}[10]}[11]}), and thus a weak starting point for a model. A better way forward, one that settles these criticisms, is afforded by a model that treats the field concept as primary. And although, for instance, some attempts have been made in the past to model relativistic theories of particles [12]}[13]}, it is by now well agreed upon that the field concept is the natural setting for relativistic theories.The book by S. Schweber [14]} has an interesting discussion on the “field versus particle" debate that occurred in the early days of quantum field theory.
